Not easy as sum of squares

Calculus Level 2

$\large \sum _{ k=1 }^{ \infty }{ \frac { 1 }{ k^{ 2 } } }$

If the series above equals to $\frac{\pi^a}b$ for positive integers $a$ and $b$ , find the value of $a+b$ .

1 solution

Shashwat Shukla
Jan 29, 2015

This is just $\zeta(2)=\frac{\pi^2}{6}$

Thus $a+b=8$ .

For proofs see: Basel Problem

As i dont know the answer to this problem so i m asking it here : Now if

${ S }_{ i }=\sum _{ k=1 }^{ \infty }{ \frac { i }{ { ({ 36k }^{ 2 }-1) }^{ i } } }$

Find ${ S }_{ 1 }+{ S }_{ 2 }$ ??????????????

(update) i have nailed it and posting it as a problem here

Gautam Sharma - 6 years, 4 months ago

U Z - 6 years, 4 months ago

Yeah! Try the problem in my above comment. And pls explain.

Gautam Sharma - 6 years, 4 months ago